@KVRaman when you compose a question, it shows you some suggestions of (what it thinks) similar questions. But you're right. I can see some classification (machine learning) techniques applicable here.
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user2468May 12 '12 at 16:31

One can also prove this by combinatorial argument. Observe that ${n \choose i}$ is the number of subsets of cardinality $i$ of a set of cardinality $n$. Then $\sum_0^n {n \choose i}$ is the number of all subsets of cardinality $0, 1, 2, \dots, n$ of a set of cardinality $n$. Hence the sum counts all subsets of a $n$-set. But we know that thare are $2^n$ subsets of such set.